Thread: Integral problem

The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.

Originally Posted by wren17

The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.

$\displaystyle \frac{dx}{dt} = t - 3 \Rightarrow x = \frac{t^2}{2} - 3t + C$.

Assume x(0) = 0: $\displaystyle x = \frac{t^2}{2} - 3t$.

Note: The answer is NOT x(4) - x(0). Why?

Distance travelled = $\displaystyle \frac{9}{2} + \left( \frac{9}{2} - 4\right) = .....$

Draw a graph of x versus t to see this.